Final thoughts before I head off to hospital (So sadly I won't be able to give any feedback for a day or two): The Infiltrator and Morphean specs for the Specialist are...really nonintuitive.If you want to use disguise stuff and fool people? No, that's not the charisma-based one. That's the wisdom one despite disguise and bluff being cha-based.
If you want to use Sense Motive and Medicine? No, that's not the wisdom based one or the Int based one. That's the cha based one? Which rather hurts the Morphean (Which already seems a bit weaker than the others). As good social stats means you can't get the talents for social infiltration...
It's not quite Exalted Sidereal Unintuitive (Why is the healing charm in archery?) but it does feel a bit backwards in areas.

Sorry about the feedback not being just 'Looks good' (Since the wis/cha lineup is...odd. Where the Wis lineup gives you cha stuff and the cha lineup gives you wis stuff. It feels a lot like it's due to legacy reasons from Pathfinder.)
(Clearly Morpheans need a ship-scale ability to make them really good at ramming ships into things)
But yeah, more seriously: While I DO understand where you are coming from it does run into the issue that the charisma-based version ends up a lot worse at the charisma-based skill than the wisdom-based one. Someone wanting to say, play James Bond, is going to have rather some issues.
I think part of it is that 'Stealth' is just such a broad thematic category.
Since you can do it in multiple ways.
Which I think is where the Morphean is having a little trouble with. 'Empath' is a much more narrow category than 'Technologist' or 'Infiltrator'.
It's personally narrow infiltrator's thematics a little to broaden Morpheans. Morphean as a name flows very naturally to a social chameleon. That is, however, just my personal preferences.
I think part of it is that Labcoat and Clipboard is a REALLY thematic Morphean thing (As you are using mind affecting to make yourself seem like you should be there. It naturally flows to an empath class)

Hmm...if I'm mathing this right, Advanced Synergy seems a tad high with the bonus to skills. It caps at +7 (Since there is the +2 from skill synergy there) rather than +6. Only a hair high but still, when they also get the rerolls it does make them terrifying at the skills. By the Numbers does seem a bit too good.
As right now it gives basicly the same bonus as the level 20 Supreme Operative (Only -1 but also level 7 vs level 20)
It's also got the upside that it applies to skill synergy skills rather than skill focus skills. As skill synergy hits twice as many skills.
Focused Disruption also seems TERRIFYING with any power with an attack roll and can lead to some massive king hits.
Was it intented to work with powers too?

Burn the Evidence seems like it's a bit too high a bonus...but it runs into the fact that well, I'm not sure what the DCs for that would BE in the first place (Is it static? Is it based on a skill check?) so it's hard to evaluate how much effect it has as a static DC would mean that it's likely ok due to non-scaling base.

Omnidisciplinary Expertise: The class already HAS 'roll twice and take the better'. Another skill reroll is a tad odd.

Lab Coat and Clipboard should likely be more about being out of character rather than illegal. f you are wandering through a devourer cult headquarters, you are ALREADY doing illegal things. They should get the second will save if you start planting flowers or doing something that doesn't involve being the dumbest motherfuckers in the setting rather than 'Here I am, worshipping the devourer in the devourer headquarters'

...overchannel is interesting with Stamina, as you'll get all your stamina back with a single resolve point outside of combat you've rarely got reason NOT to overchannel to the full extent and even in combat, unless the overchannel will punch through to Real HP you've got a lot of refreshing burnable HP.

Oh yeah: All these mind affecting things - You might want to include an option to affect constructs or undead (As they are not immune to mind affecting flat, they ARE immune to mind affecting that doesn't specify it works on them)

Waking Sleep: Basically nothing is affected by Waking Sleep right now since there is almost no abilities that care if you are out.
As an aside: Waking sleep also doesn't actually negate the -10 perception for being alseep. So your waking sleep...isn't actually very good at being awake.